Question

Rezolvați în mulțimea numerelor raționale ecuațiile:

$a) \\ \\ \frac{x}{2} - \frac{2}{3} = \frac{7}{4} \\ \\ b) \\ \\ \frac{x}{3} + \frac{5}{9} = \frac{5}{6}$

Answer 1

a)
$\frac{x}{2}-\frac{2}{3}=\frac{7}{4} \\ \\ \frac{x}{2}=\frac{7}{4}+\frac{2}{3} \\ \\ \frac{x}{2}=\frac{21}{12}+\frac{8}{12} \\ \\ \frac{x}{2}=\frac{29}{12} \\ \\ x=\frac{58}{12}=\frac{29}{6}$
b)
$\frac{x}{3}+\frac{5}{9}=\frac{5}{6} \\ \\ \frac{x}{3}=\frac{5}{6}-\frac{5}{9} \\ \\ \frac{x}{3}=\frac{15}{18}-\frac{10}{18} \\ \\ \frac{x}{3}=\frac{5}{18} \\ \\ x=\frac{15}{18}=\frac{5}{6}$